A2-web immanants

Pavlo Pylyavskyy

doi:10.1016/j.disc.2010.04.008

A₂-web immanants

Pavlo Pylyavskyy

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We describe the rank 3 Temperley-Lieb-Martin algebras in terms of Kuperberg's A₂-webs. We define consistent labelings of webs and use them to describe the coefficients of decompositions into reduced webs. We introduce web immanants, inspired by Temperley-Lieb immanants of Rhoades and Skandera. We show that web immanants are positive when evaluated on totally positive matrices and describe some further properties.

Original language	English (US)
Pages (from-to)	2183-2197
Number of pages	15
Journal	Discrete Mathematics
Volume	310
Issue number	15-16
DOIs	https://doi.org/10.1016/j.disc.2010.04.008
State	Published - Aug 28 2010
Externally published	Yes

Keywords

Immanants
Temperley-Lieb-Martin algebra
Total positivity

Publisher link

10.1016/j.disc.2010.04.008

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Cite this

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AB - We describe the rank 3 Temperley-Lieb-Martin algebras in terms of Kuperberg's A2-webs. We define consistent labelings of webs and use them to describe the coefficients of decompositions into reduced webs. We introduce web immanants, inspired by Temperley-Lieb immanants of Rhoades and Skandera. We show that web immanants are positive when evaluated on totally positive matrices and describe some further properties.

KW - Immanants

KW - Temperley-Lieb-Martin algebra

KW - Total positivity

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